I recently spoke with my best White Sox source. There’s nothing terribly exciting brewing with the club right now:
The Sox are content with their personnel this year, even more than a year ago. They’re happy with their depth and probably will not make any major deals before the deadline (ie, Andruw Jones is highly unlikely).
If they are to make a small trade, the White Sox match up well with sabermetric-type teams. Kenny Williams has made minor but helpful trades recently with Boston (David Riske) and Arizona (Alex Cintron). (And of course another not-so-small trade with Josh Byrnes for Javier Vazquez). It wouldn’t be surprising to see another small trade with that type of club. Chicago has been middle of the pack as far as relievers’ ERA, so the ’pen may have room for upgrade.
On an unrelated note, my source also indicated that the Dodgers are "kicking a lot of tires right now" and may acquire bullpen help this week.